Question Text
Question 1 :
Justify why the following quadratic equation has no two distinct real roots: $2x^2-6x+\frac{9}{2}=0$
Question 2 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 3 :
Find the roots of the following quadratic equation by factorisation: $100x^2 – 20x + 1 = 0$
Question 4 :
Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x+2=0$, by factorisation.
Question 5 :
Check whether the following is quadratic equation : (x-3)(2x + 1)= x(x+5)
Question 6 :
Check whether the following is a quadratic equation: $x(2x + 3) = x^2 + 1$
Question 7 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?
Question 8 :
Represent the following situation in the form of a quadratic equation : A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h lesss, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 9 :
Which constant should be added and subtracted to solve the quadratic equation $4x^2-\sqrt{3}x-5=0$ by the method of completing the square?
Question 10 :
State True or False whether the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
